The former prime minister, who backed the Remain campaign in the EU referendum, told Sky News his party should harden its opposition to any deal which would make Britain poorer, reaping a political windfall.
He said: "I can see a situation where the Labour Party would annihilate the Tories if it took the high ground - because it would go right back into the fundamental division within the (Conservative) Party over the future of the country.
"It would be a much more powerful political position," he argued in an interview to publicise a report by his think-tank, the Institute for Global Change.
He warned that Mr Corbyn would face the "very same political issues" faced by Theresa May if he entered Downing Street without altering Labour's stance.
"I understand the politics of this which is to say a substantial number of Labour voters voted leave so we've just got to go ahead," he said.
"But it's far better to go onto the high ground and give some leadership to our people: make their Brexit a Tory Brexit and deal with people's anxieties - whether immigration or jobs or inequality or living standards - by policies which address those questions."
He also criticised Mr Corbyn's performance in the Commons on the subject.
"We very rarely raise the topic of Brexit in Prime Minister's Questions - but it's the dominant issue of the day. So why do we do that? It's because we don't want to get into a fight on Brexit."
And Mr Blair took aim at claims in a new book by US columnist Michael Wolff, Fire and Fury: Inside the Trump White House.
Among the allegations it made were that Mr Blair wanted a job as Middle East adviser to President Donald Trump and that he warned his White House team that they were being spied on by British intelligence.
"It's just incredible the way the world works," Mr Blair said when pressed on the claims.
"I mean this is a story written in this book - by someone who's never spoken to me by the way - which is a complete fabrication.
"The notion that the British intelligence services would start spying on an American Presidential candidate - it is so ludicrous that anyone who knows anything about these (things) would know it's fatuous.
"I wasn't angling for a job. I have no desire for a job with the American administration."
Mr Blair also issued a thinly-veiled criticism of social media and news organisations, which he claimed allow misinformation to surface unchecked.
"It's halfway around the world with conspiracy theories attached to it and we will get all sorts of correspondence and tweets. The world of politics today - it's crazy how it operates."
